## Abstract

We investigate two NP-complete vertex partition problems on edge weighted complete graphs with 3k vertices. The first problem asks to partition the graph into k vertex disjoint paths of length 2 (referred to as 2-paths) such that the total weight of the paths is maximized. We present a cubic time approximation algorithm that computes a 2-path partition whose total weight is at least .5833 of the weight of an optimal partition; improving upon the (.5265 – ϵ)-approximation algorithm of [26]. Restricting the input graph to have edge weights in {0, 1}, we present a .75 approximation algorithm improving upon the .55-approximation algorithm of [16]. Combining this algorithm with a previously known approximation algorithm for the 3-Set Packing problem, we obtain a .6-approximation algorithm for the problem of partitioning a {0, 1}-edge-weighted graph into k vertex disjoint triangles of maximum total weight. The best known approximation algorithm for general weights achieves an approximation ratio of .5257 [4].

Original language | English |
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Title of host publication | Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings |

Editors | Nikhil Bansal, Irene Finocchi |

Publisher | Springer Verlag |

Pages | 953-964 |

Number of pages | 12 |

ISBN (Print) | 9783662483497 |

DOIs | |

State | Published - 2015 |

Externally published | Yes |

Event | 23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9294 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 23rd European Symposium on Algorithms, ESA 2015 |
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Country/Territory | Greece |

City | Patras |

Period | 14/09/15 → 16/09/15 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2015.

### Funding

This work is supported by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-09-2-0053, The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.

Funders | Funder number |
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U.S. Army Research Laboratory | |

Army Research Laboratory | W911NF-09-2-0053 |